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A SHARP SCHWARZ LEMMA AT THE BOUNDARY

  • AKYEL, TUGBA ;
  • ORNEK, NAFI
  • Received : 2015.05.08
  • Accepted : 2015.08.07
  • Published : 2015.08.31

Abstract

In this paper, a boundary version of Schwarz lemma is investigated. For the function holomorphic f(z) = a + cpzp + cp+1zp+1 + ... defined in the unit disc satisfying |f(z) − 1| < 1, where 0 < a < 2, we estimate a module of angular derivative at the boundary point b, f(b) = 2, by taking into account their first nonzero two Maclaurin coefficients. The sharpness of these estimates is also proved.

Keywords

Schwarz lemma on the boundary;angular limit and derivative;Julia-Wolff-Lemma;holomorphic function

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